In a large mixing bowl, whisk together the melted and cooled ghee, maple syrup, egg, egg yolk, vanilla, and almond extract for about 1 minute, until the mixture looks glossy and fully emulsified.
In a separate bowl, whisk together almond flour, arrowroot starch, baking powder, baking soda, cream of tartar, and salt until there are no visible streaks of starch.
Add the dry ingredients to the wet and mix with a wooden spoon or spatula until a soft, uniform dough forms. It should feel slightly sticky but firm enough to scoop. Cover tightly with plastic wrap and refrigerate for at least 1 hour (up to overnight) to help the dough firm and the flavors develop.
When ready to bake, preheat the oven to 350°F.
Line two baking sheets with parchment paper. Using a 2-tablespoon cookie scoop, portion 8–9 cookies per sheet, leaving 2 inches between each for spreading.
Bake for 11–12 minutes, rotating the sheets halfway through, until the cookies are puffed, lightly golden around the edges, and just set in the center.
Remove from the oven and tap the bottom of each baking sheet gently on the counter to deflate the cookies slightly for that classic soft, chewy texture.
Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely before icing.